Classification of Hard X-ray Light Curves of Black Hole Binary Transients
K. Ebisawa1 , S. Nahahira1 , T. Amagasa2 , F. Hayashi2 , Jun Fan2 , J. Sugimoto3 , A. Yoshida4
1Japan Aerospace Exploration Agency (JAXA), 2 Tsukuba University,
3
RIKEN, 4 Aoyama Gakuin University
E-mail(KE): ebisawa@isas.jaxa.jp
Abstract

We have systematically analyzed hard X-ray light curves of transient black hole binaries taken bySwift/BAT (15−50 keV) and MAXI (3−20 keV), searching for common morphological properties among
diﬀerent light curves. To that end, we have applied a technique widely used in data science, such that
virtual “distance” between two lightcurves is defined to quantify their similarities, and “tree diagram” ismade to classify all the observed lightcurves. Consequently, we have found that the lightcurves in 15−50
keV are classified into distinct groups based on their morphologies, while such a classification is not clear
in the 3−20 keV light curves. This suggests that hard X-rays are more likely to reflect distinct types of
the accretion processes in black hole binaries than soft X-rays.
Key words: black holes: light curves – MAXI – BAT – Data Science

1. Introduction
Black hole transients exhibit varieties of X-ray light
curves in terms of their morphologies, presumably reflecting various aspects of diﬀerent accretion processes.
However, our current understanding of the physicalmechanisms behind these varieties is very limited.
Both Swift/BAT and MAXI routinely produce andpublicly release the X-ray light curves of bright blackhole transients. These light curve datasets will provide
a unique opportunity to carry out systematic and unbiased studies of the black hole X-ray transient phenomena. Here, we are going to apply techniques that are
proven eﬀective in various fields of “data sciences”, andtry to classify X-ray light curves of black hole transients
based on their morphologies.
2. Data Analysis and Results
We use the Swift/BAT (15–50 keV) and MAXI (3–20 keV) publicly available X-ray light curve datasets.
We choose the following black hole (candidate) sources;
4U1630–472, GX339–4, H1743–322, MAX J1305–704,
MAXI J1543–564, MAXI J1659–152, MAXI J1836–194,
MAXI J1910–057 and XTE J1752–223. For each pair of
all the BAT light curves, we calculate their Dynamic
Time Warping (DTW) distance, which is known to be aneﬀective measure to quantify their similarities (Hayashiet al. 2013 ); we did the same for the MAXI lightcurves.
A merit of using the DTW distance is that it can findmorphological similarities between two light-curves even
if they have diﬀerent intensities or stretched in the time

direction. Based on these DTW distances, we performed
the clustering analysis to construct “tree diagrams” forBAT and MAXI light curves separately. On the tree diagram, light curves which are more similar in shape arelocated closer.
Consequently, the BAT tree diagram (Figure 1) shows
several distinct clusters, while MAXI tree diagram (notshown) does not show such clear clustering. This indicates that hard X-ray is more likely to reflect characteristics of accretion process than soft X-ray, whatever thephysical mechanisms behind. Looking at the BAT tree
diagram and those light curves belonging to each cluster,
we notice the following; besides a few “outliers”, ordinary light curves are divided into those having “doublepeaks” (Figure 2, top-left) or “single-peak”. The singlepeak light curves are further divided into “fast-decay”(top-right), “fast-rise” (bottom-right) and “slow-decay”(bottom-left) types.
Physical mechanisms behind these classifications areunclear yet. Also, it is curious why hard X-ray light
curves are more eﬀectively classified than soft ones. In
order to study their physical origins, we are investigating
for correlations between the light curve morphologicaltypes and black hole parameters, such as black hole mass,
binary parameters, luminosities and spectral states.
References
Hayashi, F. et al. 2013, Journal of Space Science
Informatics Japan: Vol.2, p.19

Fig. 1. A tree diagram to show classification of the black hole light curves taken by Swift-BAT.

Fig. 2. Four representative examples of classification of the Swift-BAT lightcurves.